Question

an atom that has the same number of neutrons as $_{56}^{138}$ba is:
$_{54}^{136}$xe
$_{55}^{138}$cs
$_{57}^{137}$la
$_{56}^{136}$ba
none of the above

Explanation:

Step1: Calculate neutrons in \(_{56}^{138}\text{Ba}\)

Number of neutrons \(N = A - Z\), where \(A\) is mass number and \(Z\) is atomic number. For \(_{56}^{138}\text{Ba}\), \(A = 138\), \(Z=56\). So \(N = 138 - 56=82\).

Step2: Calculate neutrons for \(_{54}^{136}\text{Xe}\)

For \(_{54}^{136}\text{Xe}\), \(A = 136\), \(Z = 54\). \(N=136 - 54 = 82\).

Step3: Calculate neutrons for \(_{55}^{138}\text{Cs}\)

For \(_{55}^{138}\text{Cs}\), \(A = 138\), \(Z = 55\). \(N=138 - 55=83\).

Step4: Calculate neutrons for \(_{57}^{137}\text{La}\)

For \(_{57}^{137}\text{La}\), \(A = 137\), \(Z = 57\). \(N=137 - 57 = 80\).

Step5: Calculate neutrons for \(_{56}^{136}\text{Ba}\)

For \(_{56}^{136}\text{Ba}\), \(A = 136\), \(Z = 56\). \(N=136 - 56=80\).

Answer:

\(_{54}^{136}\text{Xe}\)